ADC Guide, Part 9: Total Harmonic Distortion

Up to now, this series has primarily discussed the DC specifications
of an ADC. Now, we will talk about AC specifications like distortion
and noise in the ADC.

Total Harmonic Distortion (THD) is, as the
name suggests, the measure harmonic distortion present in a signal. It
is the ratio of the sum of the powers of all harmonic components to the
power of the fundamental frequency of the signal. THD relates to the
linearity of the system.

In part 5 of this series, we
took a brief look at how missing codes in an ADC can cause distortion in
ADC output. Such distortion will cause harmonics of the input signal to
appear in the output of the ADC. While it is true that ADC with missing
codes will have a large amount of harmonic distortion, missing codes
are not the only source of harmonic distortion. Harmonic distortion in
an ADC output is caused by any nonlinearity present in the ADC
characteristics. Every practical ADC has nonlinear characteristics. As a
result, harmonics are present in the output of every practical ADC.
While DNL and INL are the measures of nonlinearity in ADC
characteristics, THD is the measure of the resulting harmonic
distortions present in the output of an ADC.

In
order to visualize the harmonic distortion in the output of an ADC, we
would give a sine wave as an input to the ADC and plot Fourier Transform
(a.k.a. FFT) of the digital output of the ADC. Figure 1 shows an
example of the FFT of such an ADC output. Ideally, the FFT should have
had a single frequency spike at the frequency of sine wave. Although the
input signal’s frequency has the highest amplitude in the FFT plot
(green stem in the FFT), there are other frequency contents seen in the
plot. The input signal frequency is referred to as the fundamental
frequency. Apart from the fundamental frequency component, there are
spikes seen periodically in the FFT (blue stems). These are the
harmonics of the input signal frequency.

The ADC used for the measurements in Figure 1 had considerable nonlinear characteristics. For a good ADC design, the output FFT of an ADC would look much cleaner. Figure 1-1
below shows one such example. We would need more precise tools and
measuring equipment in order to characterize the distortion of such an
ADC.

Total
harmonic distortion is defined as the power of the harmonic content in
the output of ADC with respect to the power at the fundamental
frequency. It can either be expressed in decibels or percentage as per equations (1) and (2) respectively.

Click on image to enlarge.

Click on image to enlarge.

As can be seen in Figure 1,
the amplitude of the harmonics – and hence the power in the harmonic
frequencies – generally reduces as we move to higher harmonics of the
ADC. Therefore, while calculating the total harmonic distortion, only
the first few harmonics need to be considered. ADC datasheets should
specify the number of harmonics considered for calculating total
harmonic distortion numbers in the datasheet.

Apart from the fundamental frequency and harmonic frequency components of an ADC, Figure 1 also
shows the presence of some power at every other frequency component
(marked in red). This corresponds to the noise present in the output of
ADC.

In the next part of this series, we will talk about the noise specifications of an ADC.

About the authors:Sachin Gupta
is working as Product Marketing Engineer 2 with Cypress Semiconductor.
He holds a Bachelor’s degree in Electronics and Communications from Guru
Gobind Singh Indraprastha University, Delhi. He has several years of
experience in mixed signal application development. He can be reached at
sgup@cypress.com.Akshay Phatak is an Applications Engineer
with Cypress Semiconductor. He holds a Bachelor's degree in Electronics
and Telecommunications form College of Engineering, Pune (India). He
likes to work on mixed-signal embedded systems. He can be reached
at akay@cypress.com.